淡江大學覺生紀念圖書館 (TKU Library)
進階搜尋


下載電子全文限經由淡江IP使用) 
系統識別號 U0002-0407200714440700
中文論文名稱 成本限制下之最適逐步型一分群試驗
英文論文名稱 Optimal Progressive Type-I Group-Censoring Plans in Presence of Cost Constraint
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 95
學期 2
出版年 96
研究生中文姓名 廖康君
研究生英文姓名 Kang-jun Liao
學號 694460022
學位類別 碩士
語文別 中文
口試日期 2007-06-20
論文頁數 45頁
口試委員 指導教授-吳碩傑
委員-張春桃
委員-歐士田
中文關鍵字 加速壽命試驗  預算  D型最適性  費雪資訊矩陣  最大概似估計量  敏感度分析  逐步應力  韋伯分配 
英文關鍵字 Accelerated life test  Budget  D-optimality  Maximum likelihood estimation  Sensitivity analysis  Step stress  Weibull distribution 
學科別分類 學科別自然科學統計
中文摘要 在傳統的壽命試驗中,通常不允許在試驗中間移除存活之元件。但是,在實務上實驗者有時候必須於試驗中間移除部分的存活元件。因此,逐步設限便 被用來處理這種型態的問題。此外,由於試驗操作上的限制,使得有些試驗無法連續地觀察受測試元件的狀況,而只能每隔一段 時間來記錄這些元件是否發生故障,因此無法知道確切的故障時間,這種型態的資料稱為分群資料。再則由於科技的發達使得元件的可靠度不斷的提昇,所以在有限的試驗時間內可觀察到的故障元件個數便很少甚至等於零,因此加速壽命試驗的方法可讓實驗者提早獲得足夠的元件壽命資料。本論文首先將逐步設限和分群合併,提出逐步型一分群設限的試驗方式,探討在元件壽命為韋伯分配時,利用最大概似法推導出分配參數的估計及大 樣本性質。然後將試驗成本列入考量,在有限的試驗預算下,以非線性混合整數規劃方法來找出最佳的試驗配置,並舉例子來闡述所提出的方法,以及探討分配和成本參數變動時的敏感度分析。此外,本論文也將逐步應力加速壽命試驗納入研究中,提出逐步型一分群設限逐步應力加速壽命試驗計畫,並探討韋伯壽命分配下,有關參數估計的問題。然後在總預算限制下,提出建立試驗最佳配置的方法,並舉數值例子及探討相關之敏感度分析。
英文摘要 In traditional censoring life test,it is not allowed for surviving units to be removed from the test at points other than the final termination point.However, this allowance will be desirable for some experimenters.Therefore, a progressive censoring scheme is proposed to handle this problem.Besides, in practice, it is often impossible continuously to observe or inspect the testing process.
We can only record whether a test unit fails in an interval instead of measuring failure time exactly.Hence, the test units are inspected intermittently. Data of this type are called grouped data.Moreover, with today's high technology, some life tests result in few or no failures in a short life testing time.One approach to solve this problem is to accelerate the life of units by increasing the levels of stress in order to obtain failures quickly.In this thesis, we first combine progressive censoring and grouped data to develop a progressive type-I group-censoring scheme.We will use the maximum likelihood method to derive parameter estimation under Weibull failure time distribution. Furthermore, we will use the nonlinear mixed integer programming to obtain the optimal settings of a progressive type-I group-censored life test by maximizing the terminant of Fisher's information under the constraint that the total
experimental cost does not exceed a pre-determined budget.An example is discussed to illustrate the proposed method and sensitivity analysis is also studied.Finally, we will consider a step-stress accelerated life test with progressive type-I group-censoring scheme and derive the parameter estimation of Weibull distribution. The optimal design in presence of cost constraint is also investigated.
A numerical example is studied to illustrate the proposed approach and sensitivity analysis is performed.
論文目次 目錄
1.緒論-----1
1.1研究的動機與目的------1
1.2文獻回顧------3
1.3本文架構------4
2.逐步型一分群設限下壽命試驗-----6
2.1模式假設與參數估計-----6
2.2成本限制下的最佳計畫-----12
2.2.1成本函數及最佳計畫準則-----13
2.2.2決定最佳計畫之演算法------15
2.3數值分析------16
2.4敏感度分析-----17
2.4.1壽命分配參數的影響-----18
2.4.2成本參數的影響-----19
3.逐步型一分群設限逐步應力加速壽命試驗------22
3.1模式假設與參數估計-----22
3.2成本限制下的最佳計畫------30
3.2.1成本函數及最佳計畫準則------31
3.2.2決定最佳計畫之演算法-----32
3.3數值分析-----33
3.4敏感度分析-----34
3.4.1壽命分配參數的影響-----34
3.4.2成本參數的影響-----35
4.結論-----39
參考文獻-----42
表格目錄
2.1逐步型一分群設限資料------17
2.2 heta和
u在不同組合下的D型最佳設計(n,k,tau)-----20
2.3在不同成本參數下之D型最適設計(n,k,tau),theta=4.7969和
nu=1.3789-----21
3.1逐步型一分群設限下逐步應力加速的樣本------34
3.2beta_0、beta_1、sigma在不同組合下和S_h=5的最佳設計(n,k,tau)-----37
3.3在不同成本參數下之D型最適設計(n,k,tau),beta_0=2.1393、beta_1=-0.1392和sigma=0.8835和S_h=5------38
圖形目錄
2.1逐步型一分群設限之壽命試驗-----8
3.1逐步型一分群設限下應力加速壽命試驗-----24
參考文獻 Aggarwala, R. (2001).
Progressive interval censoring: some mathematical results with applications to inference,
Communications in Statistics -- Theory and Methods, 30, 1921-1935.
Bai, D.-S. and Kim, M.-S. (1993).
Optimum simple step-stress accelerated life tests for Weibull distribution and type I censoring,
Naval Research Logistics, 40, 193-210.
Balakrishnan, N. and Aggarwala, R. (2000).
it Progressive Censoring -- Theory, Methods, and Applications,Boston: Birkh"{a}user.
Balakrishnan, N. and Kim, J.-A. (2005).
Point and interval estimation for bivariate normal distribution based on progressive type-II censored data,
Communications in Statistics -- Theory and Methods, 34, 1297-1347.
Chen, J., Li, K. H. and Lam, Y. (2007). Bayesian single and double variable sampling plans for the Weibull distribution with censoring,
European Journal of Operational Research, 177, 1062-1073.
Chen, Z. and Mi, J. (1996). Confidence interval for the mean of the exponential distribution, based on grouped data,
IEEE Transactions on Reliability, 45, 671-677.
Cheng, K. F. and Chen, C. H. (1988). Estimation of the Weibull parameters with grouped data,
Communications in Statistics -- Theory and Methods, 17, 325-341.
Cohen, A. C. (1963).
Progressively censored samples in life testing,
Technometrics, 5, 327-339.
Gouno, E., Sen, A. and Balakrishnan, N. (2004).
Optimal step-stress test under progressive type-I censoring.
IEEE Transactions on Reliability, 53, 388-393.
Lawless, J. F. (2003).
Statistical Models and Methods for Lifetime Data, 2nd edition, New York: Wiley.
Lui, K. J., Steffey, D. and Pugh, J. K. (1993).
Sample size determination for grouped exponential observation: A cost function approach,
Biometrical Journal, 35, 677-688.
Meeker, W. Q. and Escobar, L. A. (1998).
Statistical Methods for Reliability Data, New York: Wiley.
Nelson, W. (1990).
Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, New York: Wiley.
Tse, S. K., Yang, C. and Yuen, H. K. (2002).
Design and analysis of survival data under an integrated type-II interval censoring scheme,
Journal of Biopharmaceutical Statistics, 12, 333-345.
Wu, S.-J. (2003).
Estimation for the two-parameter Pareto distribution under progressive censoring with uniform removals,
Journal of Statistical Computation and Simulation, 73, 125-134.
Wu, S.-J., Lin Y.-P. and Chen Y.-J. (2006).
Planning step-stress life test with progressively type I group-censored exponential data,
Statistica Neerlandica, 6, 45-56.
Yang, C. and Tse, S.-K. (2003).
Reliability sampling plans for the Weibull distribution under type II progressive censoring with binomial removals,
Journal of Applied Statistics, 30, 709-718.
Yang, C. and Tse, S.-K. (2005).
Planning accelerated life tests under progressive type I interval censoring with random removals,
Communications in Statistics -- Simulation and Computation, 34, 1001-1025.
論文使用權限
  • 同意紙本無償授權給館內讀者為學術之目的重製使用,於2008-07-05公開。
  • 同意授權瀏覽/列印電子全文服務,於2008-07-05起公開。


  • 若您有任何疑問,請與我們聯絡!
    圖書館: 請來電 (02)2621-5656 轉 2281 或 來信